Samples of cast aluminum parts are classified on the basis of surface finish (in

Question

Samples of cast aluminum parts are classified on the basis of surface finish (in microinches) and length measurements. The results of 100 parts are summarized as follows:

Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent length.

Determine:

(a) Give the exact answer.

P(A)=

(b) Give the exact answer.

P(B)=

(c) Round your answer to 4 decimal places (e.g. 98.7654).

P(A | B)=

(d) Round your answer to 4 decimal places (e.g. 98.7654).

P(B | A) =

(e) Round your answer to 4 decimal places (e.g. 98.7654).

If the selected part has excellent surface finish, what is the probability that the length is excellent?

(f) Round your answer to 4 decimal places (e.g. 98.7654).

If the selected part has good length, what is the probability that the surface finish is excellent?

Explanation / Answer

a)P(A) = (80+3)/100 = 83/100 = 0.83

b)P(B) = (80+11)/100 = 91/100 = 0.91

c)P(A/B) = P(A n B)/P(B) = (80/100)/(91/100) = 0.8/0.91 = 0.878

d)P(B/A) =  P(A n B)/P(A) =  (80/100)/(83/100) = 0.8/0.83 = 0.963

e) Probability that the length is excellent If the selected part has excellent surface finish = P(B/A) =  0.963

f)probability that the surface finish is excellent If the selected part has good length = P(A/B) = 0.878

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